Although I cannot recall the source, I was taught that the word "done" relates to food preparation (The turkey is done). On the other hand, "finished" means completed (My homework is finished).

Modern dictionaries don't seem to make this distinction. Did something change over the last 40 years?

No, nothing changed in the last forty years. They've always been perfectly acceptable synonyms. Moreover, there is not, as some have suggested above, a difference in register between the two.

Oh, sure, a few people who enjoy codifying their own shibboleths into grammatical "laws" are heard now and again to insist on a distinction--these schoolmarms have never been taken seriously by any real writer or lexicographer. You may consider it a linguistic superstition.